For much of the last century, educators and many scientists believed that children could not learn math at all before the age of five, that their brains simply were not ready.

But recent research has turned that assumption on its head — that, and a host of other conventional wisdom about geometry, reading, language and self-control in class. The findings, mostly from a branch of research called cognitive neuroscience, are helping to clarify when young brains are best able to grasp fundamental concepts.